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Convex polynomial and spline approximation inLp, O

โœ Scribed by R. A. DeVore; Y. K. Hu; D. Leviatan

Publisher
Springer
Year
1996
Tongue
English
Weight
598 KB
Volume
12
Category
Article
ISSN
0176-4276

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๐Ÿ“œ SIMILAR VOLUMES

On Positive and Copositive Polynomial an
On Positive and Copositive Polynomial and Spline Approximation inLp[โˆ’1, 1], 0<p<โˆž
โœ Y.K. Hu; K.A. Kopotun; X.M. Yu ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 610 KB

For a function f # L p [&1, 1], 0< p< , with finitely many sign changes, we construct a sequence of polynomials P n # 6 n which are copositive with f and such that & f &P n & p C| . ( f , (n+1) &1 ) p , where | . ( f , t) p denotes the Ditzian Totik modulus of continuity in L p metric. It was shown

Copositive Polynomial and Spline Approxi
Copositive Polynomial and Spline Approximation
โœ Y.K. Hu; D. Leviatan; X.M. Yu ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 439 KB

We prove that if a function \(f \in \mathbb{C}[0,1]\) changes sign finitely many times, then for any \(n\) large enough the degree of copositive approximation to \(f\) by quadratic spliners with \(n-1\) equally spaced knots can be estimated by \(C \omega_{2}(f, 1 / n)\), where \(C\) is an absolute c